10 Activities to Practice Linear Functions Like a Boss

Slope and y-intercept make up the crux of the 8th grade math standards. We spend 5 full weeks on learning slope and y-intercept and how to apply them, not to mention all the other time throughout the year getting ready to learn about them and then reviewing and applying them. It still surprises me how complex it all becomes. When you come to think of it, students have to identify slope and the y-intercept in various way. They also have to create them in various forms, and they have to be able to interpret them in many forms as well. It can reach a point of overwhelm for both the teacher and the students. Every year I pledge to myself that I will do better to help students reach the understanding they need to have and every year I get closer to that goal. In this post I’ll share ten activity ideas that get students lots of practice with using equations of linear models to solve problems.

My approach this year has taken a slight turn from years past. This time around, students spent a lot more time just understanding slope before we got into anything else. So far, they know slope better than my students in the past. Also, we’ve focused more on what the variables stand for in the slope intercept form. We’ve gone beyond just explaining it or taking notes on slope intercept form. Students review the slope intercept form and its components each day. One by one you can see a little light bulb go off for each of the students. They aren’t all there yet, but each day they move a little bit closer to the goal.

I’m going to share some of the strategies that I use or that I want to use in the future to teach students how to write equations and to help them interpret if a story is talking about slope or y-intercept. .

Let’s dive in

These activities have a wide range of uses. They can be used as the first practice that students do. Also, they work well as cyclical review down the road. They are all engaging ways to get students involved in their own learning. Most of the time they lose track of how much work they’re doing because they’re enjoying themselves at the same time.

At some point last year I realized that students just need a lot of practice writing equations from tables, stories, and graphs. One of the best ways they I know to get them this type of practice is through a maze. In these three Write an Equations mazes students solve about 13-15 problems in 10 minutes and they get the repetitions they need. It helps them see the connection between an equation and the other ways the same math problem is expressed in tables, stories, and graphs. We use mazes as our daily bell ringer in my classroom and I find that it’s a perfect warm-up.

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One year I noticed that my students in math lab really struggled to see the difference between slope and y-intercept in the real world. They seemed to be guessing every time we read a story problem about it. It sounded something like this, “This number’s the… slope? I mean, y-intercept! Yeah, that’s it, it’s the slo…intercept.” You know what I mean- when students just yell out a random answer. So, I decided that we need to break this down even further. That’s why I created this match and paste activity where all students do is look at statements and then sort them into slope or y-intercept.

We do this as a match and paste in our notebook the first time and then students have it as a reference to look back at later on. Then, I have students complete this activity a second time a couple of days later as a quick formative assessment. Also, when completing this sorting activity I have students underline the key works in each statement that let them know if it’s referring to slope or y-intercept.

This graphic organizer inside a SmartPal has been a huge hit with my students, as well as with my colleagues. The graphic organizer has a graph, a table, and a place for an equation on it. You fill-in part of the graphic organizer and students have to fill-in the rest. It challenges students to think through the different aspects of slope and y-intercept. My kids love it and every students works to try and figure it out.

Using this type of response for students gives you the opportunity to see where they struggle. I have each student show me their work after they finish. If they have it right I tell them, and if they have it wrong then they try again. Sometimes I’ll see that a third or half the class is making the same mistake. That quick formative data gives me a chance to address the misconceptions and fix it right on the spot. You can download a free copy of this graphic organizer here. Because of the strong connection between the two topics, I share more ideas about how to use this download, and the graphic organizer itself, in the post “10 Activities to Make Comparing Functions Engaging.”

I have to admit that I’ve had a hard time finding activities to practice this standard. When I can’t find an activity that fits my students’ needs, then I usually make one. That is how these task cards were born. I needed my students to get more practice, and task cards are such a versatile tool that I like to use them for every topic we study. In this set, the first 8 task cards gets students to practice writing equations from tables, graphs, and stories. The rest of the cards have students identify and write about the different parts of the slope intercept form. You can see an example below:

Task cards are so versatile. They can be used as a partner practice activity or you can save them for class warm-ups. Also, you can use them to do whole class practice with student whiteboards. Either way, usually I model the thought process for a couple of task cards before I have students start working on them.

I used this online practice for writing equations as an anticipatory set. It took a little longer than I like for anticipatory sets, but it worked great. Every student was working on a different problem at the same time and they wanted to get it right. They had to be careful about their precision and they couldn’t just throw an answer down. It seemed to help the most for the kids that have struggled to see the difference between slope and y-intercept. I think I’ll use it again in a couple of months as a review for this topic.

When you click on this download you’ll find a few different activities. There’s an activity called “Match Races with Their Equations” on page 4. They have a series of 10 stories and students write the equations. You have the option of giving the students the answers and letting them choose from the possible answers. That’s not how I use them. Instead, I really want to push my students to be able to write the equations from the stories on their own.

This download also has some other practice activities with stories, equations, and graphs. The downside is that there’s no answer key included. You could use these activities as a practice activity, homework, or an exit ticket.

This free set of task cards on Free to Discover’s blog can be used to get students more practice with linear functions. These cards feature problems that get students practice with writing linear functions from tables, finding the missing value on a table, identifying independent and dependent variables, and describing the range. You could use these task cards as warm-up problems or have students complete them with a partner for practice.

When I find worksheets like this one, I have a few go to games that I play with them just to add a little bit of excitement. My latest game is called Pick a Card. I show a problem from the worksheet on the doc cam and students work it out on their whiteboards. When everyone is ready I ask 3 to 4 questions about that problem to ask students. Questions might include:

What is the slope?

What is the y-intercept?

Describe what the slope represents.

Each student who answered gets to pick a playing card at random. Before they choose, the rest of the students have to decide who they think will get the highest card before the cards are chosen. Then, I have each of the students pick a card. When they reveal what they’ve picked, the person with the highest cards gets 1,000 points, then it’s 500 points for the second highest, and 0 for lowest. The rest of the class gets the same amount of points as the person they chose before cards were picked. It’s silly, but students get a real kick out of it and they’re more engaged when practicing the math.

By clicking on this link you’ll find 10 worksheets that will help students practice with a variety of skills related to linear functions. Some of the skills include:

Finding the slope from a graphed line

Finding the slope and y-intercept from a linear equation

Graphing lines

Working with linear equations

If you need some skill building practice, you’ll find a wide variety here. These worksheets aren’t super engaging, but there are some ways to liven them up. One thing that I do with them is use them as an exit ticket and then the next day have students analyze responses using the “My Favorite No” strategy. This means that I find the work of someone who got the question wrong, but shows a great example of a common misconception. The students have to find the mistake and fix it. Error analysis is a great way to have students think about their own math thinking.

This Stop That Creature game from PBS Kids gets students identifying the rule of functions using a table and a “function machine”. Students have to identify the rule and enter it into the machine to stop the clones. There’s a lot of cool graphics. What a fun way for kids to practice figuring out the rule of a linear function. I would use this as a fast finisher activity during my linear functions unit or as a review game later in the year.

Try one thing

With the topic of understanding linear functions, there are so many skills to practice. Don’t get overwhelmed! Remember that students just have to build on previous understanding. You don’t have to do everything all at once- you can chunk things out. Try one of the activities above and see how your student respond to it. Once you have tried one and had success then you might want to try another one. Good luck in your math teaching journey. Thanks so much for reading. Until next time!

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